A Mind For Numbers. How To Excel At Math And Science (Even If You Flunked Algebra).

When I first started to teach myself how to program, I self-diagnosed myself with dysprogrammeria - a natural inability to understand any computer language. No matter how much time and effort I invested, I could not stretch my brain enough to understand all the new concepts. I was glad to find out that the author of “A Mind For Numbers. How To Excel At Math And Science (Even If You Flunked Algebra)”, Barbara A. Oakley, must have felt similar when she first started learning engineering at the age of 23. Loathing math and science in high school, Oakley majored in Russian language and literature, taking pride in her linguistic skills and defining herself as a non-technical person. However, the situation on the job market made her reconsider her educational choices. She realized that there would always be well-paid jobs for engineers, while graduates of humanities need to struggle to get low-paid assistant positions. She decided to take classes in engineering and 30 years later, as a professor of mechanical engineering, she is sharing her experience of how to rewire a “humanistic brain” into a “technical brain”.

Even though the book has numbers in the title, there are not many references to concrete math problems. One would also be hard pressed for finding mathematical formulas or theories. It is not a tutorial or an introduction book to any specific subject. So what is this book? It is a general guide on how to learn effectively. The rules described in this book can be applied to any field that requires effortful learning of new skills, such as languages, music or programming. Oakley did a thorough research on traditional rules of learning, e.g. the rule of repetition, as well as latest findings from the fields of cognitive psychology and neuroscience and picked ones that proved to be most effective.

One of the principles presented in the book is the idea that learning is more effective when spread across longer time, with regular repetitions and time in between to consolidate knowledge. This principle is well known in psychology. But the more difficult question is how to repeat the material effectively, so that the knowledge can be later easily retrieved and flexibly applied to new problems? Oakley explains that our brain needs more time to learn, as new neural connections have to appear and to get stronger. For this stage, it is good to invest time and focused attention in trying to thoroughly understand the problem at hand: consciously concentrate on a problem, gather information, try different logical approaches. The best method is to try to solve few example problems and, if possible, compare with the provided solutions. Once the problems are really understood, it will become much easier to memorize them. However, do not get fooled with the illusion of competence - just because you understood a problem once, especially when just following someone else solving it or checking the ready solution, it does not mean that you automatically will be able to solve a similar problem in the future. For that to happen, you will need so called deliberate practice - time invested in going over different examples, pulling them apart and concentrating on parts that you find most difficult. Similar to a pianist, who first practices right hand, then left hand and then both hands together, before being able to perform a whole piece.

What is the best way to know what you do not know? Instead of passively rereading your notes, try to recall the material - it will not only show you which parts you need to practice more, but will also consolidate the material more effectively in your memory. This strategy will enable you to build mental chunks of knowledge that can be then used fast, intuitively and effortlessly. To illustrate this process, Oakley cites a study on master players in shogi - a strategy game that requires fast, mental simulation of possible moves. In the game, players have to make a decision within 2 seconds, so it is obvious that they cannot systematically consider all available options, but have to base their decision on their experience. Wan et al. (2011) have looked into the brains of the best players of shogi and found that a brain network called precuneus-caudate circuit gets activated, whenever these fast, intuitive decisions are being made. However, in order to built these circuits, one needs hours of deliberate practice. So next time, when trying to fool yourself that you can miraculously learn a new language or programming skills in a 2-week intensive course, think better of it.

Learning is in the end a lot like stretching - you are stretching your brain to adjust your current knowledge to the new information. The process is not easy and sometimes even painful. Understanding that difficulties are part of the learning process, helped me to accept the frustration. After all, programming can be tough, as it requires abstract and logical thinking. As Kenneth R. Leopold, one of the professors interviewed in the book, stated: “Befuddlement is a healthy part of the learning process. When students approach a problem and don’t know how to do it, they’ll often decide they are not good at it. (…). But the learning process is all about working your way out of confusion”. That paragraph alone motivated me to come back to my computer and stretch my brain a bit more.

There are many books about learning on the market. However, what makes Oatley’s book so good is that every suggestion she makes about how to improve the learning process is based on scientific evidence, as well as real experiences of people that she had interviewed. She is not trying to “sell” any fashionable, new methods with no proven effectiveness, but instead concentrates on things that work and tries to explain how to use them best. There are also many illustrations of the principles explained, some illustrations better than others. For example, procrastination habits are portrayed as brain-eating zombies. I am personally not a big zombie fan, but some people might find it convincing. Other than that, the book is very well written, without excessive scientific jargon. It is not a quick read though. It you want to benefit from advice in the book, I would suggest reading it chapter by chapter and trying to immediately incorporate the advice in your learning routine. You will not learn math just by reading this book. You will still need to invest many, many hours in practice. But by following the advice from the book, I am sure that you can make your practice much more effective.